Jamal has a utility function u=w12u=w12, where ww is his wealth in millions of dollars and uu is the utility he obtains from that wealth. in the final stage of a game show, the host offers jamal a choice between (a) $4 million for sure, or (b) a gamble that pays $1 million with probability 0.6 and $9 million with probability

The expected of both offers are:

Offer A's expected price = $4 million

Offer B's expected price = ($1 million x 0.6) + ($9 million x 0.4) = $4.2 million

Jamal's utility function U = W¹/² or U = √W

Offer A's expected utility = √$4,000,000 = 2,000 utils

Offer B's expected utility = √$4,200,000 = 2,049 utils

Both the difference in expected value and utility is not that large, but the difference in risk is great, so if I was Jamal I would choose option A.